An auctioneer typically has to make a number of decisions when designing an auction. Similarly, a bidder participating in an auction must also make a number of decisions when determining a bid. In order to assist an auctioneer or a bidder in making their respective decisions, various tools have been developed for analyzing a particular market environment. One set of tools provides for estimating bidder's valuations for an auctioned object based on historical bids. The theory of Affiliated Private Value (APV) auction models is one of these tools.
In some prior art methods, it is assumed that there is no asymmetry across different segments of bidders. These unnecessary assumptions limit the applicability if the model to a limited number of specific auction environments. Since most auctions comprise asymmetries among bidder segments, this theory is limited in accurate applicability.
One prior art method for an asymmetric model requires K+1 dimensional kernel estimation, where K is the number of asymmetric bidder segments. Even with just two asymmetric bidder segments, at least 3-dimensional kernel estimation has to be used. As the dimensionality goes up, kernel density method requires much more number of data samples to achieve the same quality (variance) of estimation. As such, this method requires substantial computation. Table 1 illustrates how the rate of the number of samples required increases as the dimensionality becomes higher.
TABLE 1DimensionalityNumber of Samples14219367422371070010842000
As shown in Table 1, a very large number of data samples is required to produce an accurate estimation of bid valuation. For just two types of asymmetric bidders, the current method requires 67 samples. For three types of asymmetric bidders, the current method requires 223 samples. Often, auctions comprise relatively few participants and occur infrequently. As such, it may not be possible to obtain enough data samples from historical bid data to obtain the estimation of bid valuation.
Current methods for determining bidders' valuations for an auctioned object based on historical bid data have substantial drawbacks. One class of methods requires the use of broad assumptions to determine the bidders' valuations, thus limiting the applicability and reliability of the results. Furthermore, other methods require substantial data and heavy computation to determine the bidders' valuations. The amount of data required is typically not available, limiting the usefulness of this method.